User blog:Cheetahrock63/Viridery Omniverse
an underwhelming result of using Hypercomplex stuff to worldbuild WIP The Viridery Omniverse is a small omniverse that contains many archverses all infinite in size each with 1 spatial dimension and 1 temporal dimension strung together in a "quilt"-like fashion, in a sense. The universes all follow special relativity and take on the form of 1+1-dimensional Minkowski planes. The beings living within the omniverse are in the shapes of line segments and points. Structure Viridery is a small omniverse both in the sense that it is small for an omniverse in comparison to other omniverses explored in the wiki and that it is a Small Omniverse⁠—an archverse with index ω. Any given universe can be modeled as the split-complex line—the transformations that take a reference frame and transform it to the frame that moves at a constant velocity v (where v is always less than the speed of light c ) are Lorentz transformations. The Lorentz transform of a point p (position x = \Re (p) and time t = \Im (p) ), p' , is defined as so: p' = p \cdot (\cosh ({\rm {arctanh}} (v)) - {\acute{j}} \sinh ({\rm {arctanh}} (v))) . Split-complex maps of z \cdot (\cosh ({\rm {arctanh}} (v)) - {\acute{j}} \sinh ({\rm {arctanh}} (v))) serve as useful visualizations, they serve as "spacetime globes". Worldlines of a particle moving at a velocity less than c are modeled as lines of the form \{x+{\acute{j}}f(x) \in {\mathbb {D}}:\forall t \in {\mathbb {R}}(1 , curves in the split-complex line always with a slope greater than 1. Stationary objects have a worldline that is a vertical line. Light rays are slanted lines at an angle of 45°. The light cone is the set of all split-complex numbers with a modulus of zero \{z \in {\mathbb {D}}:|z|=0\} . A Penrose diagram is the end result of a transformation that takes the infinite Minkowski plane and transforms it into an area of finite size while preserving light-rays being 45° diagonal lines. The relationship between a point on the split-complex line p and the Penrose diagram p' is \arctan (p) = p' where \arctan is the principal value of the inverse tangent. The split-complex map of \arctan is a way to represent a Penrose diagram of a Minkowski universe. The resulting Penrose diagram is a square with vertices at (\pm \frac{\pi}{2},0) and (0,\pm \frac{\pi}{2}) . The vertices (\pm \frac{\pi}{2},0) are the "spacelike infinities" of the universe, the vertices (0,\pm \frac{\pi}{2}) are the "timelike infinities" of the universe, and the edges of the Penrose diagram are the "lightlike infinities" of the universe. Now it's time for the real cosmological fantasy stuff. So, \arctan is not the only value of the inverse tangent. In general, \forall z \in {\rm {D}}(\tan (\arctan (z) + n_0\pi + n_1\pi{\acute{j}}): n_0 + n_1 \in {\mathbb {Z}} = z) . A split-complex map for all branches of \arctan or equivalently, the contour map of \tan over the split-complex numbers visually looks like a "quilt" of Penrose diagrams of universe stitched together by the lightlike infinities. This can be called a visualization of a "multiverse" that comprises of an infinite number of universes. Apparently something about other universes and wormholes is done using Penrose diagrams, but I really do not know enough about anything to really do anything about it. File:Split-complex tan(tan(z)).png|Contour plot of \tan (\tan (z)) over the split-complex numbers. File:Tantansplit.png|Contour map of split-complex \tan with null cones in orange, "light cones at infinity" in black, and "essential cones" in purple. Continuing the pattern, you can consider "megaverses" by considering the contour map of \tan (\tan (\tan (z))) over the split-complex numbers, “gigaverses" by considering \tan (\tan (\tan (\tan (z)))) , “teraverses" by considering \tan (tan (\tan (\tan (\tan (z))))) , and so on. For any n+1 -verse for natural n , you can consider the contour map of split-complex \tan iterated n -times. Entities The entities living in Viridery consist of point-creatures and line-creatures known as Xantha (singular Xanthon) and Cyatela (singular Cyatelon) respectively. Xantha and Cyatela are characterized by their abilities to pass through one another and communicate with any given member of their species in their local Multiverse. Xantha and Cyatela can communicate with each other but generally only if they live in the same universe. There are of course, extremely rare exceptions where Xantha and Cyatela can communicate to those living outside of their own multiverse. Such creatures are sometimes called “'Extraversal'”. While technically there is the same number of extraversal creatures as non-extraversal creatures, they are distributed very differently with extraversals being far more sparse than non-extraversals. In Viridery Megaverse 0’s cohort of more than a million multiverses, there is thought to be only one Extraversal xanthon. Xantha and Cyatela commune telepathically. However, xantha are far more susceptible than cyatela to decaying if they talk to those outside of their universe for too long. Many suspect that this is because xantha are much smaller and generally much weaker than cyatela. Category:Blog posts